Integrable geodesic flows with simultaneously diagonalisable quadratic integrals
Differential Geometry
2026-04-07 v1 Mathematical Physics
Dynamical Systems
math.MP
Exactly Solvable and Integrable Systems
Abstract
We show that if functionally independent commutative quadratic in momenta integrals for the geodesic flow of a Riemannian or pseudo-Riemannian metric on an -dimensional manifold are simultaneously diagonalisable at the tangent space to every point, then they come from the St\"ackel construction, so the metric admits orthogonal separation of variables.
Cite
@article{arxiv.2403.14319,
title = {Integrable geodesic flows with simultaneously diagonalisable quadratic integrals},
author = {Sergey I. Agafonov and Vladimir S. Matveev},
journal= {arXiv preprint arXiv:2403.14319},
year = {2026}
}